Stewart made no mistake from 12 yards but his colleagues - notably Christian Nade, David Templeton and Obua himself - were less accurate in front of goal and as a result meant the visitors were in the game until the end.
Hearts' defence stood firm though as Csaba Laszlo's side maintained their recent revival to consolidate fifth position in the league.
Obua said: "We were trying to get a second goal to make it easier for us and I had a chance but cut in and just misfired my shot.
"But the most important thing was that we won the game and got three more points in the league.
"Whenever you win you are happy because even if it's just 1-0 that's all you need to do. We got our goal and then we played well in defence after that.
"The fans were a bit anxious at the end which is understandable but you just have to block that out of your mind and keep on playing to make sure you get the right result."
Laszlo claims tight victories such as the one over St Mirren are crucial for the development of his young side.
During his time at the club, Laszlo has seen a host of experienced players leave and is having to mould a new side based around younger players such as Scott Robinson, Gordon Smith and the talented Templeton.
Laszlo said: "When you have a lot of young guys in the team you lose a bit of nerve. We have good young players like Scott Robinson and David Templeton but they lack experience.
"Football at this level is more than just about having the ability, it is also about having concentration and awareness.
"So that is why I was very happy to beat St Mirren because it helps with confidence and allows the players to develop without having the critics talking about them.
"If you get a win at the weekend having worked with the players during the week it is a big positive as they believe in what they are doing.
"Last season we had a lot of experience with players like Robbie Neilson and other national players from their country. Now we have Gordon Smith, Scott Robinson and David Templeton - maybe they will be the next national players for their country?"
Laszlo has also admitted he does not know if he will be able to add to his squad during the January transfer window.
He said: "We still have two weeks to bring someone in and I hope that is that case and I am very positive about it but for now I am concentrating on the team which beat St Mirren."
Meanwhile St Mirren manager Gus MacPherson believes the SPL is as tight a league as he has ever known.
MacPherson has played in and managed in the top flight for many years but feels there is little to choose between the teams at the top and the bottom.
He said: "The fine lines in this league are shown by the fact on the last day of last season we could have been relegated but could also have finished ninth.
"That's as tight as the games are and as tight as the league is. Five or six points will make an enormous difference.
"That's when you know that one goal from a set piece can make a big difference to your season.
"That's just how tight the games are at the moment. So many are being settled by one goal or a set piece because the teams are all so closely matched."
Scottish Premier Winner 2009/10 Win Outright: Hearts 400/1
Source: Team Talk
Source: Team Talk